SOLUTION: Find the exponential equation whose graph passes through the points (-1, 1/2 ) and (2,32)

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Question 1158809: Find the exponential equation whose graph passes through the points (-1, 1/2 ) and (2,32)
Found 2 solutions by MathLover1, greenestamps:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!


y+=+a%2Ab%5Ex......use the point (-1, 1%2F2 )
1%2F2+=+a%2Ab%5E-1
1%2F2+=+a%2Fb
b=2a..........eq.1

32+=+a%2A%282a%29%5E2.....using the point (2,32)
32=+a%2A4a%5E2
32=4a%5E3
8=a%5E3
a=root%283%2C8%29
a=root%283%2C2%5E3%29
a=+2.........eq.2

substitute in eq.1

b=2a..........eq.1
b=2%2A2
b=4

your equation is:
y+=++2%2A4%5Ex




Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The general form is y+=+ab%5Ex

Form equations using both given points:
1%2F2+=+ab%5E%28-1%29
32+=+ab%5E2

Divide the second equation by the first to eliminate a:
64+=+b%5E3
b+=+4

Use this b value in either original equation to determine a:
32+=+a%284%5E2%29
32+=+16a
a+=+2

a=2; b=4. The equation is

y+=+2%284%5Ex%29